Built on

Andrew M. Childs and Yuan Su, Nearly optimal lattice simulation by product formulas , Physical Review Letters 123
Original
1901
Earlier work this paper cites.
Ian D. Kivlichan, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Wei Sun, Zhang Jiang, Nicholas Rubin, Austin Fowler, Alán Aspuru-Guzik, Hartmut Neven, and Ryan Babbush, Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via Trotterization , Quantum 4
Original
1902
Earlier work this paper cites.
Tianyi Peng, Aram W. Harrow, Maris Ozols, and Xiaodi Wu, Simulating large quantum circuits on a small quantum computer , Physical Review Letters 125
Original
1904
Earlier work this paper cites.
Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe, Time-dependent Hamiltonian simulation with L 1 L^{1} -norm scaling , Quantum 4
Original
1906
Earlier work this paper cites.
Chi-Fang Chen and Andrew Lucas, Finite speed of quantum scrambling with long range interactions , Physical Review Letters 123
Original
1907
Earlier work this paper cites.
Guang Hao Low, Vadym Kliuchnikov, and Nathan Wiebe, Well-conditioned multiproduct Hamiltonian simulation , 2019, arXiv:1907.11679
Original
1907
Earlier work this paper cites.
Tomotaka Kuwahara and Keiji Saito, Strictly linear light cones in long-range interacting systems of arbitrary dimensions , Physical Review X 10
Original
1910
Earlier work this paper cites.
Yingkai Ouyang, David R. White, and Earl T. Campbell, Compilation by stochastic Hamiltonian sparsification , Quantum 4
Original
1910
Earlier work this paper cites.
Elliott H. Lieb and Derek W. Robinson, The finite group velocity of quantum spin systems , Communications in Mathematical Physics 28
1972
Earlier work this paper cites.
Richard P. Feynman, Simulating physics with computers , International Journal of Theoretical Physics 21
1982
Earlier work this paper cites.
John Day Dollard and Charles N. Friedman, Product integration with application to differential equations , Cambridge University Press, 1984
1984
Earlier work this paper cites.
Masuo Suzuki, Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics , Journal of Mathematical Physics 26
1985
Earlier work this paper cites.
Stanley C. Eisenstat and Ilse C. F. Ipsen, Relative perturbation techniques for singular value problems , SIAM Journal on Numerical Analysis 32
1988
Earlier work this paper cites.
J. Huyghebaert and H. De Raedt, Product formula methods for time-dependent Schrödinger problems , Journal of Physics A: Mathematical and General 23
1990
Earlier work this paper cites.
Masuo Suzuki, General theory of fractal path integrals with applications to many-body theories and statistical physics , Journal of Mathematical Physics 32
1991
Earlier work this paper cites.
Robert I. McLachlan, On the numerical integration of ordinary differential equations by symmetric composition methods , SIAM Journal on Scientific Computing 16
1995
Earlier work this paper cites.
Seth Lloyd, Universal quantum simulators , Science 273
1996
Earlier work this paper cites.
Ilse C. F. Ipsen, Relative perturbation results for matrix eigenvalues and singular values , Acta Numerica 7
1998
Earlier work this paper cites.
Tobias Jahnke and Christian Lubich, Error bounds for exponential operator splittings , BIT Numerical Mathematics 40
2000
Earlier work this paper cites.
Robert I. McLachlan and G. Reinout W. Quispel, Splitting methods , Acta Numerica 11
2002
Earlier work this paper cites.
Alexander F. Shaw, Pavel Lougovski, Jesse R. Stryker, and Nathan Wiebe, Quantum algorithms for simulating the lattice Schwinger model , Quantum 4
Original
2002
Earlier work this paper cites.
Dorit Aharonov and Amnon Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge , Proceedings of the 35th ACM Symposium on Theory of Computing, pp. 20–29, 2003, arXiv:quant-ph/0301023
2003
Earlier work this paper cites.
Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, and Daniel A. Spielman, Exponential algorithmic speedup by quantum walk , Proceedings of the 35th ACM Symposium on Theory of Computing, pp. 59–68, 2003, arXiv:quant-ph/0209131
2003
Earlier work this paper cites.
Laura Clinton, Johannes Bausch, and Toby Cubitt, Hamiltonian simulation algorithms for near-term quantum hardware , 2020, arXiv:2003.06886
Original
2003
Earlier work this paper cites.
Anthony W. Knapp, Basic real analysis , Birkhëuser, 2005
2005
Earlier work this paper cites.
Ernst Hairer, Christian Lubich, and Gerhard Wanner, Geometric numerical integration: structure-preserving algorithms for ordinary differential equations , vol. 31, Springer Science & Business Media, 2006
2006
Earlier work this paper cites.
Matthew B. Hastings and Tohru Koma, Spectral gap and exponential decay of correlations , Communications in Mathematical Physics 265
2006
Earlier work this paper cites.
Bruno Nachtergaele, Yoshiko Ogata, and Robert Sims, Propagation of correlations in quantum lattice systems , Journal of Statistical Physics 124
2006
Earlier work this paper cites.
Bruno Nachtergaele and Robert Sims, Lieb-Robinson bounds and the exponential clustering theorem , Communications in Mathematical Physics 265
2006
Earlier work this paper cites.
Burak Şahinoğlu and Rolando D. Somma, Hamiltonian simulation in the low energy subspace , 2020, arXiv:2006.02660
Original
2006
Earlier work this paper cites.
Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, Faster digital quantum simulation by symmetry protection , to appear in PRX Quantum (2021), arXiv:2006.16248
Original
2006
Earlier work this paper cites.

Similar

Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders, Efficient quantum algorithms for simulating sparse Hamiltonians , Communications in Mathematical Physics 270
2007
Cited alongside, same era.
Jad C. Halimeh, Haifeng Lang, Julius Mildenberger, Zhang Jiang, and Philipp Hauke, Gauge-symmetry protection using single-body terms , 2020, arXiv:2007.00668
Original
2007
Cited alongside, same era.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, A quantum algorithm for the Hamiltonian NAND tree , Theory of Computing 4
2008
Cited alongside, same era.
Shenglong Xu, Leonard Susskind, Yuan Su, and Brian Swingle, A sparse model of quantum holography , 2020, arXiv:2008.02303
Original
2008
Cited alongside, same era.
Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd, Quantum algorithm for linear systems of equations , Physical Review Letters 103

Then

David-Maximilian Storch, Mauritz Van Den Worm, and Michael Kastner, Interplay of soundcone and supersonic propagation in lattice models with power law interactions , New Journal of Physics 17
Original
2015
Later among the works it cites.
Dave Wecker, Matthew B. Hastings, Nathan Wiebe, Bryan K. Clark, Chetan Nayak, and Matthias Troyer, Solving strongly correlated electron models on a quantum computer , Physical Review A 92
Original
2015
Later among the works it cites.
Sergio Blanes and Fernando Casas, A concise introduction to geometric numerical integration , Chapman and Hall/CRC, 2016
2016
Later among the works it cites.
Rolando D. Somma, A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation , Journal of Mathematical Physics 57
Original
2016
Later among the works it cites.
Yosi Atia and Dorit Aharonov, Fast-forwarding of Hamiltonians and exponentially precise measurements , Nature communications 8

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2019

A Theory of Trotter Error

Childs, Andrew M., Su, Yuan, Tran, Minh C. et al.

Understand

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators.

Despite significant effort, the error scaling of such product formulas remains poorly understood.
We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion.
Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions.

Built on

Andrew M. Childs and Yuan Su, Nearly optimal lattice simulation by product formulas , Physical Review Letters 123
Original
1901
Earlier work this paper cites.
Ian D. Kivlichan, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Wei Sun, Zhang Jiang, Nicholas Rubin, Austin Fowler, Alán Aspuru-Guzik, Hartmut Neven, and Ryan Babbush, Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via Trotterization , Quantum 4
Original
1902
Earlier work this paper cites.
Tianyi Peng, Aram W. Harrow, Maris Ozols, and Xiaodi Wu, Simulating large quantum circuits on a small quantum computer , Physical Review Letters 125
Original
1904
Earlier work this paper cites.
Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe, Time-dependent Hamiltonian simulation with L 1 L^{1} -norm scaling , Quantum 4
Original
1906
Earlier work this paper cites.
Chi-Fang Chen and Andrew Lucas, Finite speed of quantum scrambling with long range interactions , Physical Review Letters 123
Original
1907
Earlier work this paper cites.
Guang Hao Low, Vadym Kliuchnikov, and Nathan Wiebe, Well-conditioned multiproduct Hamiltonian simulation , 2019, arXiv:1907.11679
Original
1907
Earlier work this paper cites.
Tomotaka Kuwahara and Keiji Saito, Strictly linear light cones in long-range interacting systems of arbitrary dimensions , Physical Review X 10
Original
1910
Earlier work this paper cites.
Yingkai Ouyang, David R. White, and Earl T. Campbell, Compilation by stochastic Hamiltonian sparsification , Quantum 4
Original
1910
Earlier work this paper cites.
Elliott H. Lieb and Derek W. Robinson, The finite group velocity of quantum spin systems , Communications in Mathematical Physics 28
1972
Earlier work this paper cites.
Richard P. Feynman, Simulating physics with computers , International Journal of Theoretical Physics 21
1982
Earlier work this paper cites.
John Day Dollard and Charles N. Friedman, Product integration with application to differential equations , Cambridge University Press, 1984
1984
Earlier work this paper cites.
Masuo Suzuki, Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics , Journal of Mathematical Physics 26
1985
Earlier work this paper cites.
Stanley C. Eisenstat and Ilse C. F. Ipsen, Relative perturbation techniques for singular value problems , SIAM Journal on Numerical Analysis 32
1988
Earlier work this paper cites.
J. Huyghebaert and H. De Raedt, Product formula methods for time-dependent Schrödinger problems , Journal of Physics A: Mathematical and General 23
1990
Earlier work this paper cites.
Masuo Suzuki, General theory of fractal path integrals with applications to many-body theories and statistical physics , Journal of Mathematical Physics 32
1991
Earlier work this paper cites.
Robert I. McLachlan, On the numerical integration of ordinary differential equations by symmetric composition methods , SIAM Journal on Scientific Computing 16
1995
Earlier work this paper cites.
Seth Lloyd, Universal quantum simulators , Science 273
1996
Earlier work this paper cites.
Ilse C. F. Ipsen, Relative perturbation results for matrix eigenvalues and singular values , Acta Numerica 7
1998
Earlier work this paper cites.
Tobias Jahnke and Christian Lubich, Error bounds for exponential operator splittings , BIT Numerical Mathematics 40
2000
Earlier work this paper cites.
Robert I. McLachlan and G. Reinout W. Quispel, Splitting methods , Acta Numerica 11
2002
Earlier work this paper cites.
Alexander F. Shaw, Pavel Lougovski, Jesse R. Stryker, and Nathan Wiebe, Quantum algorithms for simulating the lattice Schwinger model , Quantum 4
Original
2002
Earlier work this paper cites.
Dorit Aharonov and Amnon Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge , Proceedings of the 35th ACM Symposium on Theory of Computing, pp. 20–29, 2003, arXiv:quant-ph/0301023
2003
Earlier work this paper cites.
Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, and Daniel A. Spielman, Exponential algorithmic speedup by quantum walk , Proceedings of the 35th ACM Symposium on Theory of Computing, pp. 59–68, 2003, arXiv:quant-ph/0209131
2003
Earlier work this paper cites.
Laura Clinton, Johannes Bausch, and Toby Cubitt, Hamiltonian simulation algorithms for near-term quantum hardware , 2020, arXiv:2003.06886
Original
2003
Earlier work this paper cites.
Anthony W. Knapp, Basic real analysis , Birkhëuser, 2005
2005
Earlier work this paper cites.
Ernst Hairer, Christian Lubich, and Gerhard Wanner, Geometric numerical integration: structure-preserving algorithms for ordinary differential equations , vol. 31, Springer Science & Business Media, 2006
2006
Earlier work this paper cites.
Matthew B. Hastings and Tohru Koma, Spectral gap and exponential decay of correlations , Communications in Mathematical Physics 265
2006
Earlier work this paper cites.
Bruno Nachtergaele, Yoshiko Ogata, and Robert Sims, Propagation of correlations in quantum lattice systems , Journal of Statistical Physics 124
2006
Earlier work this paper cites.
Bruno Nachtergaele and Robert Sims, Lieb-Robinson bounds and the exponential clustering theorem , Communications in Mathematical Physics 265
2006
Earlier work this paper cites.
Burak Şahinoğlu and Rolando D. Somma, Hamiltonian simulation in the low energy subspace , 2020, arXiv:2006.02660
Original
2006
Earlier work this paper cites.
Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, Faster digital quantum simulation by symmetry protection , to appear in PRX Quantum (2021), arXiv:2006.16248
Original
2006
Earlier work this paper cites.

Similar

Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders, Efficient quantum algorithms for simulating sparse Hamiltonians , Communications in Mathematical Physics 270
2007
Cited alongside, same era.
Jad C. Halimeh, Haifeng Lang, Julius Mildenberger, Zhang Jiang, and Philipp Hauke, Gauge-symmetry protection using single-body terms , 2020, arXiv:2007.00668
Original
2007
Cited alongside, same era.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, A quantum algorithm for the Hamiltonian NAND tree , Theory of Computing 4
2008
Cited alongside, same era.
Shenglong Xu, Leonard Susskind, Yuan Su, and Brian Swingle, A sparse model of quantum holography , 2020, arXiv:2008.02303
Original
2008
Cited alongside, same era.
Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd, Quantum algorithm for linear systems of equations , Physical Review Letters 103

Then

David-Maximilian Storch, Mauritz Van Den Worm, and Michael Kastner, Interplay of soundcone and supersonic propagation in lattice models with power law interactions , New Journal of Physics 17
Original
2015
Later among the works it cites.
Dave Wecker, Matthew B. Hastings, Nathan Wiebe, Bryan K. Clark, Chetan Nayak, and Matthias Troyer, Solving strongly correlated electron models on a quantum computer , Physical Review A 92
Original
2015
Later among the works it cites.
Sergio Blanes and Fernando Casas, A concise introduction to geometric numerical integration , Chapman and Hall/CRC, 2016
2016
Later among the works it cites.
Rolando D. Somma, A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation , Journal of Mathematical Physics 57
Original
2016
Later among the works it cites.
Yosi Atia and Dorit Aharonov, Fast-forwarding of Hamiltonians and exponentially precise measurements , Nature communications 8

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2009

Cited alongside, same era.

Stéphane Descombes and Mechthild Thalhammer, An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime , BIT Numerical Mathematics 50

2010

Cited alongside, same era.

Benjamin P. Lanyon, James D. Whitfield, Geoff G. Gillett, Michael E. Goggin, Marcelo P. Almeida, Ivan Kassal, Jacob D. Biamonte, Masoud Mohseni, Ben J. Powell, Marco Barbieri, Alán Aspuru-Guzik, and Andrew G. White, Towards quantum chemistry on a quantum computer , Nature chemistry 2

Original

2010

Cited alongside, same era.

Nathan Wiebe, Dominic W. Berry, Peter Høyer, and Barry C. Sanders, Higher order decompositions of ordered operator exponentials , Journal of Physics A 43

Original

2010

Cited alongside, same era.

David Poulin, Angie Qarry, Rolando D. Somma, and Frank Verstraete, Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space , Physical Review Letters 106

Original

2011

Cited alongside, same era.

Dong An, Di Fang, and Lin Lin, Time-dependent unbounded Hamiltonian simulation with vector norm scaling , 2020, arXiv:2012.13105

Original

2012

Cited alongside, same era.

Andrew M. Childs and Nathan Wiebe, Hamiltonian simulation using linear combinations of unitary operations , Quantum Information & Computation 12

Original

2012

Cited alongside, same era.

Roger A. Horn and Charles R. Johnson, Matrix analysis , Cambridge university press, 2012

2012

Cited alongside, same era.

Original

2017